05
Mar
05

### Flame Fractal

Flame Fractals are a popular, generalized variation of IFS fractals, invented by Scott Draves. This one is based on the ApophysisPOV-Ray code.
```(* runtime: 25 seconds *) V1[{x_, y_}] := {Sin[x], Sin[y]}; F1[p_] := Module[{p2 = {{0.81, -0.33}, {0.08, 0.89}}.p + {0.24, -0.07}}, 0.88p2 + 0.12V1[p2]]; F2[p_] := Module[{p2 = {{0.3, 0.52}, {-0.56, 0.37}}.p + {-0.09, -0.42}}, 0.88p2 + 0.12V1[p2]]; F3[p_] := V1[{{-0.43, 0.38}, {-0.2, -0.44}}.p + {1.74, 1.21}]; F4[p_] := V1[{{-0.49, -0.27}, {0.28, -0.53}}.p + {0.51, 0.62}]; w1 = 0.65; w2 = 0.29; w3 = 0.03; w4 = 0.03; n = 275; image = Table[{0, 0, 0}, {n}, {n}]; p = {0, 0}; Do[x = Random[]; k = Which[x < w1, 1, x < w1 + w2, 2, x < w1 + w2 + w3, 3, True, 4]; p = {F1, F2, F3, F4}[[k]][p]; {j,i} = Round[n{p[[1]] + 1.1, p[[2]] + 1.8}/3]; image[[i, j]] += List @@ ToColor[Hue[k/4.0], RGBColor], {100000}]; Show[Graphics[RasterArray[Map[RGBColor @@ Map[(1 - Exp[-0.2#]) &, #] &, image, {2}]], AspectRatio -> 1]];```

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